[dynamics_in_one_dimension] Editorial Suggestions

[pgrosser1]

Comments by @Jiarui-ZH, @jstac and I:

Content

• Change the order of the lectures 21. The Solow-Swan Growth Model and 22. Dynamics in One Dimension
• 21.1 - State that 1-δ is an assumption of the model
• 21.1 - Explain what α is
• 21.1 - Clarify the derivation of ( k_{t+1} ) by write out an extra step of dividing both step by L
• 21.2 - Include a comparative study to see changes in the shape of the model as A or K changes
• 21.3 - Might consider giving some further exploitation for the diagram in this section
• Remove the discussion of the Solow-Swan model from Dynamics in One Dimension (ie. Section 22.4), refer an example to the Solow-Swan Growth Model lecture
• 22.2.2 - add an explanation about what "sending a set S back onto itself" means, ie. by graphing the examples and by mentioning that if x is in S, then g(x) will also be in S
• 22.3.1 - add further explanation about the steady state conditions for the simple model presented, ie. that the model simplifies if a = 1 and b = 0
• 22.3.3 - add a diagram to supplement the local stability discussion
• 22.3.3 - local stability is defined as the derivative of the function being negative when evaluated at the fixed point
• Add a summarising paragraph --> broader link to chaotic dynamics through the trajectories (ie. period-n cycles)

[HumphreyYang]

Comments by @longye-tian:

Content

• Give some motivations in the first section by finding a very simple linear dynamics
• If $n$ is an integer -> if $n$ is a positive integer
• Change the duplicated heading for 22.2.3. Dynamic systems.
• Explain what is $g_0$. Also, we should use $g^n$ instead of $g^t$
• Capitalize the first letter in the section headings.
• where $a, b$ are fixed constants -> where $a, b$ are constants. Sometimes they are referred to as parameters
• $t \geq 0$ -> t = 0, 1, 2
• Arbitrary $t$ to non-negative integer $t$
• For example, recall how we previously studied -> For example, in the simple Solow-Swan growth model.
• $k$ is capital stock -> $k$ is capital stock per capita
• a fixed dynamic system consisting -> a dynamic system consisting
• Use commas instead of full stops below the sentence: "For example, for the linear model $x_{t+1} = a x_t + b$, you can use the definition to check that"
• Give an example of locally stable steady state in 22.3.3. Local stability
• 45 degree -> 45-degree
• Limitations of 45-degree diagram in terms of high dimensional and stochastic dynamics

Code

• Add labels to axis in plot45 function x_t and x_{t+1}
• Put the global variables into function $g$
• Missing full stop in 'study the trajectories'

[mmcky]

@longye-tian would you be able to take a look at the other suggestions in this issue and given them a go.

[longye-tian]

This issue is closed and followed up by #526 .